Finite Amplitude Waves on Aircraft Trailing Vortices

1972 ◽  
Vol 23 (4) ◽  
pp. 307-314 ◽  
Author(s):  
D W Moore
Keyword(s):  
Numerical Methods ◽  
Linear Theory ◽  
Finite Amplitude ◽  
Detailed Structure ◽  
The Core ◽  
Trailing Vortices ◽  
Finite Amplitude Waves

SummaryNumerical methods are used to study the growth of waves of finite amplitude on a pair of parallel infinite vortices. The vortices are treated as lines except in so far as the detailed structure of the core is needed to remove consistently the singularity in the line integrals for the velocities of the vortices. It is shown that the vortices eventually touch and the shape of the wave at this instant is calculated. The wave is quite distorted at this instant, but it is shown that its gross properties are given roughly by linear theory.

A theory of the propagation of internal gravity waves of finite amplitude

1969 ◽  
Vol 39 (3) ◽  
pp. 497-509 ◽  
Author(s):  
B. S. H. Rarity
Keyword(s):  
Energy Density ◽  
Linear Theory ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Ray Theory ◽  
Conservation Equations ◽  
Geometrical Representation ◽  
Non Linear ◽  
Finite Amplitude Waves

A non-linear theory of internal gravity waves of finite amplitude is developed in terms of conservation equations averaged with respect to the phase. The theory overcomes the failure of linear ray theory in regions in which waves are trapped and establishes the conditions under which finite amplitude waves may propagate. It gives a geometrical representation of the degeneration of waves into quasi-turbulence and predicts the dependence of the energy density on its parameters.

A WEAKLY NONLINEAR INSTABILITY OF MISCIBLE DISPLACEMENTS IN A RECTILINEAR POROUS MEDIA FLOW

1994 ◽  
Vol 04 (05) ◽  
pp. 1319-1328 ◽  
Author(s):  
WILLIAM B. ZIMMERMAN
Keyword(s):  
Linear Theory ◽  
Landau Equation ◽  
Separation Of Variables ◽  
Finite Amplitude ◽  
Linear Stability Theory ◽  
Porous Media Flow ◽  
Perturbation Scheme ◽  
Viscous Effects ◽  
Regular Perturbation ◽  
Displacement Front

The linear stability theory of Tan & Homsy [1986] is extended to include the effects of weak nonlinear coupling between mass flux and viscous effects when the viscous fingers grow from a slowly diffusing, nearly flat displacement front. A regular perturbation scheme combined with a similarity-separation of variables technique leads to a Landau equation for the amplitude of the disturbance. The Landau constant has a simple pole for a given wavenumber within the linear theory cutoff wavenumber for growth. An argument is given that this pole leads to pairing of fingers while the instability remains small. Comparison of the length scale of the pole of the Landau constant with experimental measurements of finger scale shows good agreement where plausibly finite-amplitude effects might come into play, but with the linear theory otherwise.

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

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